In the NY State DMV website, I read that vehicle owners must register their vehicles within 180 days of the effective date on their Insurance ID Cards. But how many days can I wait before I get my insurance? I cannot find the information in the insurance requirements.
Zero days, under a literal and strict reading of New York Vehicle and Traffic Law § 319. As is typical, the DMV does not accurately say what the law is, they only paraphrase a regulation that they wrote that is related to the law. The law simply says that to operate a vehicle in NY, you have to have insurance of a bond. Violation yields a fine of $150-$1500, 15 days in prison, or both. There is no provision that says "you may delay getting insurance for N days". When the DMV says "To register a vehicle in New York State you must have New York State issued automobile liability insurance coverage", they are not accurately saying what the fundamental law is – have insurance, period. Them refusing to register a vehicle without insurance is a way to enforce the law (via § 312), but it doesn't mean that you can skip the insurance if you're unregistered.
It is worthwhile to consider why this is so. If you don't have the required insurance, then you might smack somebody and do damage, and the victim would have no practical way of recovering their damages. This would clearly be a problem, and therefore it is, as far as I know, a universal requirement in the US that you absolutely must have liability insurance (or a bond) to drive, so that you can live up to your legal obligations in case you cause damage. The state's interest in registering vehicles is entirely separate (as a revenue-generating scheme and means of establishing ownership). You are required to have insurance even to drive through New York; you are not required to register your vehicle to drive through. So insurance is really about the liability, and not the registration: connecting it to registration is just a means of enforcing the law.